# Number System (Test 3)

## Problem Solving And Reasoning : Mathematics Or Quantitative Aptitude

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Number System
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Q.1
If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
A. 0
B. 1
C. 2
D. None of these
Explaination / Solution:

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.

x = 2.

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Q.2
The smallest 3 digit prime number is:
A. 101
B. 103
C. 109
D. 113
Explaination / Solution:

The smallest 3-digit number is 100, which is divisible by 2.

100 is not a prime number.

101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.

101 is a prime number.

Hence 101 is the smallest 3-digit prime number.

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Q.3
Which one of the following numbers is exactly divisible by 11?
A. 235641
B. 245642
C. 315624
D. 415624
Explaination / Solution:

(4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.

(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.

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Q.4
(?) - 19657 - 33994 = 9999
A. 63650
B. 53760
C. 59640
D. 61560
E. None of these
Explaination / Solution:

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Q.5
The sum of first 45 natural numbers is:
A. 1035
B. 1280
C. 2070
D. 2140
Explaination / Solution:

Let Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.

 Sn = n [2a + (n - 1)d] = 45 x [2 x 1 + (45 - 1) x 1] = 45 x 46 = (45 x 23) 2 2 2

= 45 x (20 + 3)

= 45 x 20 + 45 x 3

= 900 + 135

= 1035.

Shorcut Method:

 Sn = n(n + 1) = 45(45 + 1) = 1035. 2 2

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Q.6
Which of the following number is divisible by 24 ?
A. 35718
B. 63810
C. 537804
D. 3125736
Explaination / Solution:

24 = 3 x8, where 3 and 8 co-prime.

Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.

Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.

Consider option (D),

Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.

Also, 736 is divisible by 8.

3125736 is divisible by (3 x 8), i.e., 24.

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Q.7
 753 x 753 + 247 x 247 - 753 x 247 = ? 753 x 753 x 753 + 247 x 247 x 247
A. 1/1000
B. 1/506
C. 253/500
D. None of these
Explaination / Solution:

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Q.8
(?) + 3699 + 1985 - 2047 = 31111
A. 34748
B. 27474
C. 30154
D. 27574
E. None of these
Explaination / Solution:

x + 3699 + 1985 - 2047 = 31111

x + 3699 + 1985 = 31111 + 2047

x + 5684 = 33158

x = 33158 - 5684 = 27474.

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Q.9
If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:
A. 2
B. 5
C. 6
D. 7
Explaination / Solution:

Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.

x = 7.

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Q.10
The difference between the local value and the face value of 7 in the numeral 32675149 is
A. 75142
B. 64851
C. 5149
D. 69993
E. None of these